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Accuracy and Stability of Numerical Algorithms

Accuracy and Stability of Numerical Algorithms

2nd Edition

£63.00

  • Date Published: August 2002
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • format: Hardback
  • isbn: 9780898715217

£ 63.00
Hardback

This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
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About the Authors
  • This book gives a thorough, up-to-date treatment of the behaviour of numerical algorithms in finite precision arithmetic. It combines algorithmic derivations, perturbation theory, and rounding error analysis, all enlivened by historical perspective and informative quotations. The coverage of the first edition has been expanded and updated, involving numerous improvements. Two new chapters treat symmetric indefinite systems and skew-symmetric systems, and nonlinear systems and Newton's method. Twelve new sections include coverage of additional error bounds for Gaussian elimination, rank revealing LU factorizations, weighted and constrained least squares problems, and the fused multiply-add operation found on some modern computer architectures. This new edition is a suitable reference for an advanced course and can also be used at all levels as a supplementary text from which to draw examples, historical perspective, statements of results, and exercises. In addition the thorough indexes and extensive, up-to-date bibliography are in a readily accessible form.

    • Not designed specifically as a textbook, although this new edition is a suitable reference for an advanced course
    • Can also be used by instructors at all levels as a supplementary text from which to draw examples, historical perspective, statements of results, and exercises
    • With its thorough indexes and extensive, up-to-date bibliography, the book provides a mine of information in a readily accessible form
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    Reviews & endorsements

    'This book is a monumental work on the analysis of rounding error and will serve as a new standard textbook on this subject, especially for linear computation.' S. Hitotumatu, Mathematical Reviews

    '…This definitive source on the accuracy and stability of numerical algorithms is quite a bargain and a worthwhile addition to the library of any statistician heavily involved in computing.' Robert L. Strawderman, Journal of the American Statistical Association

    '…A monumental book that should be on the bookshelf of anyone engaged in numerics, be it as a specialist or as a user.' A. van der Sluis, ITW Nieuws

    'This text may become the new 'Bible' about accuracy and stability for the solution of systems of linear equations. It covers 688 pages carefully collected, investigated, and written … One will find that this book is a very suitable and comprehensive reference for research in numerical linear algebra, software usage and development, and for numerical linear algebra courses.' N. Köckler, Zentrallblatt für Mathematik

    '… Nick Higham has assembled an enormous amount of important and useful material in a coherent, readable form. His book belongs on the shelf of anyone who has more than a casual interest in rounding error and matrix computations. I hope the author will give us the 600-odd page sequel. But if not, he has more than earned his respite - and our gratitude.' G. W. Stewart, SIAM Review

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    Product details

    • Edition: 2nd Edition
    • Date Published: August 2002
    • format: Hardback
    • isbn: 9780898715217
    • length: 710 pages
    • dimensions: 260 x 181 x 37 mm
    • weight: 1.39kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • Table of Contents

    Preface
    1. Principles of finite precision computation
    2. Floating point arithmetic
    3. Basics
    4. Summation
    5. Polynomials
    6. Norms
    7. Perturbation theory for linear systems
    8. Triangular systems
    9. LU factorization and linear equations
    10. Cholesky factorization
    11. Symmetric indefinite and skew-symmetric systems
    12. Iterative refinement
    13. Block LU factorization
    14. Matrix inversion
    15. Condition number estimation
    16. The Sylvester equation
    17. Stationary iterative methods
    18. Matrix powers
    19. QR factorization
    20. The least squares problem
    21. Underdetermined systems
    22. Vandermonde systems
    23. Fast matrix multiplication
    24. The fast Fourier transform and applications
    25. Nonlinear systems and Newton's method
    26. Automatic error analysis
    27. Software issues in floating point arithmetic
    28. A gallery of test matrices
    Appendices
    Bibliography
    Name index
    Subject index.

  • Author

    Nicholas J. Higham, University of Manchester

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